Answer:
They now should survey 800 people.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
In this problem:
Same level of confidence, so same z
Same proportion, so same
We have to change n
We want to reduce the margin of error by half.
M is inverse proportion to the square root of n. That is, as n increases, M decreases.
We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4
The first survey had a sample of 200 people
Increasing by a factor of 4.
200*4 = 800
They now should survey 800 people.